Fractal-Fractional Modeling Strategies for Math Anxiety Using Hadamard Derivatives Study

Abstract

In this paper, we propose a novel mathematical model utilizing fractal-fractional calculus, specifically employing the Hadamard derivative, to gain a deeper understanding of the dynamics of math anxiety. This approach allows us to incorporate both the fractal structure of cognitive processes and the non-local (memory) effects inherent in emotional responses. We conduct an extensive literature survey, identify key research gaps, formulate a new mathematical model, perform qualitative analysis to assess the stability and existence of solutions, develop a numerical scheme based on the Hadamard operator, and simulate the model under various scenarios. Our results demonstrate that the fractal-fractional model provides a more realistic representation of math anxiety dynamics compared to classical integer-order models. © 2026 NSP.